PIRSA:15020078 Scientific Series Quantum Fields and Strings

DOI10.48660/15020078

Series: Quantum Fields and Strings

(2015). Tensor Networks from Integral Geometry. Perimeter Institute. https://pirsa.org/15020078

Tensor Networks from Integral Geometry. Perimeter Institute, Feb. 24, 2015, https://pirsa.org/15020078 

@misc{ pirsa_PIRSA:15020078,
  doi = {10.48660/15020078},
  url = {https://pirsa.org/15020078},
  author = {},
  keywords = {Quantum Fields and Strings},
  language = {en},
  title = {Tensor Networks from Integral Geometry},
  publisher = {Perimeter Institute},
  year = {2015},
  month = {feb},
  note = {PIRSA:15020078 see, \url{https://pirsa.org}}
}

Abstract

The analogy between Multi-scale Entanglement Renormalization
Ansatz (MERA) and the spatial slice of three-dimensional anti-de
Sitter space (AdS3) has motivated a great interest in tensor networks
among holographers. I discuss a way to promote this analogy to a
rigorous, quantitative, and constructive relation. A key quantitative
ingredient is the way the strong subadditivity of entanglement entropy
is encoded in MERA and in a holographic spacetime. The upshot is that
the map between MERA and the spatial slice of AdS3 is mediated through
an additional integral transform. Interpreted directly, MERA is a
discretization not of the spatial slice of AdS3, but of the space of
geodesics on the spatial slice of AdS3.

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